First mate has no taste for company (4)
I believe the answer is:
firm
'company' is the definition.
(thesaurus)
'first mate has no taste' is the wordplay.
'has no' indicates named letters should be taken away.
'first'+'mate'='firstmate'
'firstmate' with 'taste' removed is 'FIRM'.
'for' is the link.
(Other definitions for firm that I've seen before include "solid structure" , "commercial partnership" , "Company; steady" , "Unflinching" , "Steady and resolute" .)